Starter mathematicians might think everything is math.
Senior mathematicians lose their sleep whenever they think about what our math is missing and they don’t know what it is yet
The universe is actually a computer program
The mind is actually a computer program
When someone has a hammer everything looks like a nail.
When someone is paid a lot of money because they have that hammer, the belief that everything is a nail seems backed by self-assigned genius and unique insight.
Do we have ways of computing orders of infinity higher than ℵ₀?
Crap. Markdown isn’t markdowning. Fixed with unicode.
Symbolically, sure, but then you’re not dealing with infinities you’re just representing them.
It’s a meme it’s playing fast and loose with things but the general gist is that mathematics, to this day, doesn’t really care about Gödel/Church/Turing, incompleteness, the halting problem, whatever angle you want to look at it from. Formalists lost the war and they simply went on doing maths as if nothing had happened, as if a system could be simultaneously complete and consistent. There’s people out there preaching to the unenlightened masses but it’s an uphill battle.
Math went on because it doesn’t matter. Nobody cares about incompleteness. If you can prove ZFC is inconsistent, do it and we’ll all move to a new system and most of us wouldn’t even notice (since nobody references the axioms outside of set theorists and logicians anyway). If you can prove it’s incomplete, do it and nobody will care since the culprit will be an arcane theorem far outside the realm of non-logic fields of math.
